By qualifying the 21-year-old, the Oilers would maintain his rights if he decides to play in Europe next season - something the winger's agent said will happen if he isn't traded away from Edmonton.
Oilers general manager Ken Holland said recently that he'll only deal Puljujarvi if it makes sense for the team.
After being selected by Edmonton with the fourth overall pick of the 2016 draft, Puljujarvi has struggled to carve out a role, contributing just 17 goals and 37 points in 139 career contests.
The qualifying offer to Puljujarvi must include a 5 percent raise, or just over $874,000, Spector added.
Teams have until 5 p.m. ET on June 25 to extend qualifying offers to their restricted free agents.